Polygenic selection to a changing optimum under self–fertilisation

Many traits are polygenic, affected by multiple genetic variants throughout the genome. Selection acting on these traits involves co–ordinated allele–frequency changes at these underlying variants, and this process has been extensively studied in random–mating populations. Yet many species self–fertilise to some degree, which incurs changes to genetic diversity, recombination and genome segregation. These factors cumulatively influence how polygenic selection is realised in nature. Here, we use analytical modelling and stochastic simulations to investigate to what extent self–fertilisation affects polygenic adaptation to a new environment. Our analytical solutions show that while selfing can increase adaptation to an optimum, it incurs linkage disequilibrium that can slow down the initial spread of favoured mutations due to selection interference, and favours the fixation of alleles with opposing trait effects. Simulations show that while selection interference is present, high levels of selfing (at least 90%) aids adaptation to a new optimum, showing a higher long–term fitness. If mutations are pleiotropic then only a few major–effect variants fix along with many neutral hitchhikers, with a transient increase in linkage disequilibrium. These results show potential advantages to self–fertilisation when adapting to a new environment, and how the mating system affects the genetic composition of polygenic selection.


Gradual optimum shift, no background selection
In natural populations, it is also possible for organisms to experience a gradual optimum shift.This can occur if, for example, the environment changes slowly due to changes in the local environment or climate.This model also reflects cases where an organism is slowly expanding its range into new regions.A gradual optimum shift could also affect the LD structure in highly selfing species, due to the continual need to adapt over time.We hence ran simulations with a gradually-changing optimum to determine how this affected the nature of polygenic adaptation in selfing species, focusing only on the non-pleiotropic case.Genetic variance is slightly higher overall in the rescaled-outcrossing population, caused by a higher additive variance and LD covariance of a lower magnitude.
Given that inbreeding variance is non-zero under the high selfing case, these results suggest that the inbreeding-based reduction in recombination causes a greater loss in trait variation than expected under simply reducing the recombination rate, reflecting purging of selected variants.
With recessive deleterious mutations included (Figure M), genic and genetic variance is higher under outcrossing, but LD covariance is more strongly negative.We also observe that the mean fitness is greatly reduced in the outcrossing case, and inbreeding depression has increased.Overall, this result suggests that low-recombination outcrossers more strongly suffer from selection interference, so recessive deleterious mutations persist leading to reduced fitness.This interference also means that trait variants with compensatory effects are more likely to be found on the same haplotypes.Conversely, these recessive deleterious mutations are purged under high self-fertilisation.

Haplotype structure
By inspecting the LD decay under the rescaled outcrossing case, we obtain further evidence that LD clustering does not occur to the same degree as under the high selfing case.In particular, when deleterious mutations are absent, then we do not observe persistence of LD over the same large distances as under high selfing Figure A: As Figure 5 in the main text but plotting |D ′ | as a function of distance.
Adaptation takes longer in line with the gradual change in optimum value (Figure B(a)).There is a noticeable dip in mean fitness during this adaptation phase; we also observe a rise in the variance in fitness.After 100 generations, we observe similar results to the instant-optimum-shift case, with high self-fertilising exhibiting the highest mean fitness and lowest inbreeding depression and fitness variance.Variance measurements (Figure B(b)) and haplotype plots (Figure B(b)) are qualitatively similar to the instant-shift case.Mean LD values appear constant over time as in the instant-shift case, but there's an appearance in high-LD cases later on at 1,000 generations (Figure D).
Figure B: (a) Mean fitness, (b) variance measurements where there is a gradual change in the fitness optimum and pleiotropy is absent.

FigureFigureFigure I :
Figure C: (a), (b) Haplotype plots and (c), (d) following a gradual change in optimum shift when mutations are not pleiotropic.Populations are either (a) outcrossing or (b) 99.9% self-fertilising.
Figure K: As Figure 1 in the main text, but comparing the S = 0.999 case to an outcrossing population with rescaled mutation, recombination rates.
Figure N: LD decay for outcrossing populations with rescaled recombination, mutation rates to match those in a highly selfing population.Cases considered are (a) no deleterious mutations or pleiotropy; (b) no deleterious mutations, pleiotropy present; or (c) deleterious mutations (with h = 0.2) and pleiotropy absent.

Figure O :
Figure O: Haplotype plots (a), (b) and LD heatmaps (c), (d) for outcrossing populations with rescaled recombination, mutation rates to match those in a highly selfing population.There are no background deleterious mutations, and pleiotropy is either absent (a) (c) or present (b) (d).